Evolutionary Algorithm for Bandstop Frequency SelectiveSurface

The Fifth IEEE International Conferenceon Communications and Electronics

Evolutionary Optimization for Bandstop FrequencySelective Surface

Linh Ho Manh, Marco Mussetta, Riccardo E.ZichDepartment of Energy, Politecnico di Milano, Italy

July 31st, 2014

OUTLINE

Introduction and Motivation

Frequency Selective Surface by multi-layer microstrip structureAdvantages of proposed solution

Heuristic Optimization

Conventional PSOMeta-PSO as a class of variation

Frequency Selective Surface

Floquet TheoremNumerical results

[email protected] IEEE ICCE 2014

Frequency Selective Surface as A Spatial Filter

Figure: Radomes to reduce the radar cross-section (RCS) at theCryptologic Operations Center, Misawa, Japan

Once being exposed to electromagnetic radiation, a FSS behaveslike a spatial filter, some frequency bands are transmitted and some

are prohibited.


Different shapes printed a dielectric substrate

Figure: A variety of FSS elements over the past decade

The dual rectangular ring configuration printed on FR4 substrate isconsidered for WiFi bandstop filter, prohibited band ranging from2.4 GHz to 2.5 GHz.


Frequency behavior of complementary FSS structures

Figure: a) Patch type has capacitive response whereas b) Slot type hasinductive response


FSS as a periodic structure

Figure: Top view of the unit cell in a periodic FSS

As shown in Figure 4, the solution domain consists of 7 variables:a,a1, b1, t1, t2, a2 ,b2; which are properly modeled to satisfy thefeasibility of fabrication.


Advantages of proposed solution

i) Many degrees of freedom to adjust thanks to the dual ringconfiguration

ii) Easy deployment since the shapes construction arestraightforward

iii) Wider bandwidth can be achieved by proper tuning ofgeometrical parameters (this procedure is controlled by Globaloptimizer)


Conventional PSO

Conventional PSO algorithm can be briefly introduced by a set oftwo equations:

Vi(k+1) = (k)Vi

(k) + c11(Pi Xi(k)) + c22(GXi(k)) (1)Xi

(k+1) = Xi(k) +Vi

(k+1) (2)

Figure: Updating velocity rules for Conventional Particle SwarmOptimization


Undifferentiated Meta-PSOs

The idea of Meta-PSO is to use multiple swarms to enhance thecapabilities of global search, but adopt different simple rules tomanipulate the interactions among them.

Figure: Updating velocity rules for Undifferentiated Meta-PSO


Differentiated Meta-PSOs

iLj is the index to denote Absolute leader Meta-PSO or

democratic leader Meta-PSO

Figure: Updating velocity rules for Differentiated Meta-PSO


Comparisons between Conventional PSO and Meta-PSO

Test for a standard cost function:

c = 1Ni=1

sin(pi(xi 3))pi(xi 3) (3)

the objective is to minimize cost value c

Figure: Capability of PSO and Meta-PSO for a specific and simpleproblem


Optimization Scheme

Each set of geometrical parameters stands for one specific FSSconfiguration. What full-wave simulation returns will be used toevaluate the structure. After a certain number of loops, the optimaldesign is retrieved.

Figure: Optimization scheme with the link between the 3D full-waveanalysis and global optimizer


Floquet Theorem for a 1D problem

Considering a 1D periodic surface in x with the period d, in whichu(x) stands for a field reacting with this structure.

u(x+ d) = Cu(x)

u(x+ 2d) = Cu(x+ d)

...

...

u(x+ nd) = Cu(x+ (n 1)d) (4)The formulas in equation 4 can be express generally as:

u(x+ nd) = Cnu(x) (5)

For boundedness and EM fields: C = e+jkd. We can define aperiodic function P (x), where

P (x) = ejkxu(x) (6)


Consequently from equation 6, we have:

P (x+ d) = ejk(x+d)u(x+ d) = ejk(x+d)Cu(x)

= ejkxejkd(ejkd

)u(x) = ejkxu(x) = P (x) (7)

Similarly, P (x+ nd) = P (x)1. P(x) is a periodic function in x, with the period d2. Since P (x) is periodic in x, we can express it via Fourier Series

P (x) =

n=

pnej 2pindx (8)

Substituting equation 6, then

u(x) =

n=pne

jkxnx (9)

in which:kxn = k +

2pin

d(10)


Equation 10 represents harmonic expansion of the field u(x), eachterm in Equation 9 stands for a spatial Floquet Harmonic, whichpropagates along the periodic axis. Based on Floquets theorem,any planar periodic function can be expanded as an infinitesuperposition of Floquet harmonics.

Figure: Organizing FSS as a planar periodic structure


Frequency Selective Surface solved as a 3D Floquetproblem

In the restricted scope of this research, all the unit cells are squareby parameter a. FSS structure is illuminated by plane waves withpropagation direction normal to the planar surface and no phasedelays are introduced between adjacent elements.


Numerical results

When behaving bandstop characteristics, the requirements ofS21 < 10 dB and S11 > 1 dB should be fulfilled.

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 640

35

30

25

20

15

10

5

0

Frequency (GHz) >

(dB)

>

S11S21WiFi band

Figure: Frequency response of best configuration ever found by optimizer


The objective is to enlarge the bandstop region, prohibitedbandwidth (BW) is related to cost value according to theformulation:

Cost Value = 100 +BW/2 (11)

0 5 100

50

100

150Cost Function Max Value

Iteration0 5 10

0

50

100

150Cost Function Mean Value

Iteration

Figure: The Max and Mean Value throughout 10 iterations


Optimal FSS design

Details of optimal parameters are presented in Table 1.

Table: Optmizied geometrical parameters by Meta-PSO

Parameter a a1 b1 t1 t2 a2 b2Values 36.7 27.456 27.659 0.756 1.9 8.7 10.071

911 simulations were evaluated by Meta-PSO optimizer inapproximately 35 hours. Commercial full-wave analysis isimplemented on an Intel(R) core I-7 2600 CPU, 3.4 GHz, 8 GbRam system.


Extension of the case

in order to create a reverse behavior of a spatial bandpass filter, theidea is to make a reverse structure.

Figure: Top view of the unit cell for a bandpass FSS



Introduction and MotivationFrequency Selective Surface by multi-layer microstrip structureAdvantages of proposed solution

Heuristic OptimizationConventional PSOMeta-PSO as a class of variation

Frequency Selective SurfaceFloquet TheoremNumerical results

Documents

Evolutionary Algorithm for Bandstop Frequency SelectiveSurface